Logarithmic approximants: Difference between revisions

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Tuning the octave pure while preserving the ratios specified above yields, respectively, 31edo, 19edo and 34edo.
Tuning the octave pure while preserving the ratios specified above yields, respectively, 31edo, 19edo and 34edo.


Tuning the intervals <u>9/7</u>, <u>7/5</u> and <u>5/3</u> in the ratio of their approximants (1/8 : 1/6 : 1/4 = 3 : 4 : 6) and adjusting their sum to a perfect twelfth yields the [[Bohlen-Pierce|equally tempered Bohlen-Pierce scale]].
Tuning the intervals <u>9/7</u>, <u>7/5</u> and <u>5/3</u> in the ratio of their approximants (1/8 : 1/6 : 1/4 = 3 : 4 : 6) and adjusting their sum to a perfect twelfth yields the equally tempered [[Bohlen–Pierce scale]].


Tuning the intervals <u>11/9</u>, <u>9/7</u>, <u>3/2</u> and <u>5/3</u> in the ratio of their approximants (1/10 : 1/8 : 1/5 : 1/4 = 4 : 5 : 8 : 10) and adjusting their sum to a major tenth yields [[88cET|88 cent equal temperament]].
Tuning the intervals <u>11/9</u>, <u>9/7</u>, <u>3/2</u> and <u>5/3</u> in the ratio of their approximants (1/10 : 1/8 : 1/5 : 1/4 = 4 : 5 : 8 : 10) and adjusting their sum to a major tenth yields [[88cET|88 cent equal temperament]].